Dynamic light scattering (DLS) experiments were performed on stretched sheets of liquid crystal elastomers (LCEs) swollen with a nematic solvent with different swelling ratios. We show that the obtained stress-strain curve and DLS data can still be explained with the concepts of semisoft elasticity. The stress-strain curve shows a typical semisoft response with a threshold strain and a plateau region where stress increases only a little with the applied strain. The width of the plateau decreases with the increase of the swelling ratio because the polymer backbone anisotropy reduces during the swelling. The relaxation rate of thermally excited director fluctuations, however, still shows a typical response, and our measurements indicate the presence of a soft dynamic director-shear mode, as predicted by the theory of semisoft elasticity.